Information-theoretic measures of uncertainty for interval-set decision tables

Abstract

Uncertainty measurement is considered as a vital quantitative way for analyzing and mining potential characteristic features in different types of decision tables. However, considering the equivalent relation is not suitable for evaluating the relationships of objects, few studies focused on the interval-set decision tables. In this paper, we address the uncertainty measurement problem in interval-set decision tables. Firstly, a similarity relation is induced by the similarity degree. Based on the similarity relation, a notion of granular structure is defined and the corresponding properties are investigated in interval-set decision tables. Secondly, we extend the accuracy and the roughness, called the interval approximation accuracy and the interval approximation roughness, to measure the uncertainty under the granular structures. By the analysis of the two extended measures, they can effectively evaluate the uncertainty caused by the approximations in the rough set model. Considering that the size of similarity classes can also affect the uncertainty, an alternative uncertainty measure based on the conditional information entropy, called the interval-decision entropy, is proposed. Moreover, a definition of reduct based on our proposed measure is provided and a heuristic attribute reduction algorithm is designed. Finally, numerical experiments demonstrate that the proposed uncertainty measures are effective and suitable for interval-set decision tables.